# Using Newton's 2nd Law to find acceleration

• PerpetuallyConfused
In summary, the problem involves a snowboarder sliding down an incline with an initial velocity of 5.0 m/s and a 28 degree angle. The coefficient of kinetic friction is 0.18 and the snowboarder comes to rest after sliding 110 meters. The task is to use Newton's second law to find the acceleration of the snowboarder while on the incline and on the flat surface. After drawing a free body diagram, the acceleration on the incline is found to be 3.04 m/s^2. The acceleration on the flat surface is not needed as the snowboarder will have some remaining velocity that gets dissipated. However, it can be calculated using the same formula for the incl
PerpetuallyConfused
So this is my first time posting on here and I hope I'm doing right!

1. Homework Statement

A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28 ∘ incline. After sliding down the 110-mlong incline (on which the coefficient of kinetic friction is μk = 0.18), the snowboarder has attained a velocity v. The snowboarder then slides along a flat surface (on which μk = 0.15) and comes to rest after a distance x.

Use Newton's second law to find the snowboarder's acceleration while on the incline and while on the flat surface.

F_net = ma

## The Attempt at a Solution

I already drew a free body diagram when the snowboarder is on the incline with the normal force perpendicular to the slope, the force of gravity is pointing downwards, and the force of kinetic friction is pointing parallel to the slope. I know I need to use F_net = ma but I'm still very confused on how to set it up. I'm also having trouble deciding the coordinate system to use and how it relates to finding F_net.

PerpetuallyConfused said:
So this is my first time posting on here and I hope I'm doing right!

1. Homework Statement

A 75-kg snowboarder has an initial velocity of 5.0 m/s at the top of a 28 ∘ incline. After sliding down the 110-mlong incline (on which the coefficient of kinetic friction is μk = 0.18), the snowboarder has attained a velocity v. The snowboarder then slides along a flat surface (on which μk = 0.15) and comes to rest after a distance x.

Use Newton's second law to find the snowboarder's acceleration while on the incline and while on the flat surface.

F_net = ma

## The Attempt at a Solution

I already drew a free body diagram when the snowboarder is on the incline with the normal force perpendicular to the slope, the force of gravity is pointing downwards, and the force of kinetic friction is pointing parallel to the slope. I know I need to use F_net = ma but I'm still very confused on how to set it up. I'm also having trouble deciding the coordinate system to use and how it relates to finding F_net.

It sounds like you have set it up. What do you have for the forces on the snowboarder? Can you calculate those?

You don't need a coordinate system as such.

PeroK said:
It sounds like you have set it up. What do you have for the forces on the snowboarder? Can you calculate those?

You don't need a coordinate system as such.
Ok, I actually figured out how to find the acceleration while on the incline.
It was a = 9.8sin(28) - (0.18)(9.8)cos(28) which equaled 3.04 m/s^2

But now I'm having trouble figuring out how to find the acceleration while on a flat surface.

You don't necessarily need the acceleration on the flat. At the bottom he will have some velocity or energy that gets dissipated as he slows down.

PerpetuallyConfused said:
Ok, I actually figured out how to find the acceleration while on the incline.
It was a = 9.8sin(28) - (0.18)(9.8)cos(28) which equaled 3.04 m/s^2

But now I'm having trouble figuring out how to find the acceleration while on a flat surface.

Isn't the flat surface easier?

In fact, isn't a flat surface just an incline with an angle of 0?

PeroK said:
Isn't the flat surface easier?

In fact, isn't a flat surface just an incline with an angle of 0?

Ah, yes. That makes sense haha. I got the right answer. Thanks for your help!

## What is Newton's 2nd Law?

Newton's 2nd Law, also known as the law of acceleration, states that the acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to its mass.

## How do I use Newton's 2nd Law to find acceleration?

To use Newton's 2nd Law to find acceleration, you must first identify the net force acting on the object and its mass. Then, you can use the formula a = F/m to calculate the acceleration.

## What are the units of measurement for acceleration in Newton's 2nd Law?

The units of measurement for acceleration in Newton's 2nd Law are meters per second squared (m/s²).

## What is the difference between mass and weight in Newton's 2nd Law?

Mass and weight are often used interchangeably, but they are actually two different concepts in Newton's 2nd Law. Mass refers to the amount of matter in an object, while weight is a measure of the force of gravity acting on an object. The mass of an object remains constant, but its weight can change depending on the strength of the gravitational field it is in.

## Can Newton's 2nd Law be applied to all types of motion?

Yes, Newton's 2nd Law can be applied to all types of motion, including linear, circular, and rotational motion. As long as there is a net force acting on an object, its acceleration can be calculated using this law.

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